Mixed-Effects Models
Disturbance through human hunting activity can significantly impact prey species through both consumptive and nonconsumptive effects. The nonconsumptive effects of rabbit hunting on Northern Bobwhite (Colinus virginianus; hereafter, bobwhite) could cause an increased perceived risk of predation by bobwhite during rabbit hunting events may elicit anti-predator responses, such as reduced movement away from the safety of cover, among bobwhite.
bobwhite <- read.csv('bobwhite3.csv')
bobwhite$ID <- as.factor(bobwhite$ID) #make ID a factor
p1<- ggplot(bobwhite, aes(x=HuntDay, y=HW_Dist, group=ID, color=ID, shape=ID)) +
geom_point(size=4, alpha=0.6, position = position_dodge2(width=.33, preserve = "total")) +
scale_y_continuous() +
#geom_line() +
geom_smooth(method = "lm", se = FALSE) +
labs(title="Risk Behavior in Bobwhite During Hunting Season", x= "Hunting Season Species", y = "Distance from Hardwood Forest Cover (meters)")+
theme_bw()
p1## `geom_smooth()` using formula 'y ~ x'
# ID: Unique ID given to each bobwhite covey tracked in chronological order.
# HuntDay: Denotes if it was a “Rabbit” or “Quail” (bobwhite) scheduled hunt day.
# HW_Dist: Distance in meters a bobwhite covey was from hardwood habitat.bobwhite_means <- bobwhite %>%
group_by(HuntDay) %>%
summarise(mean_HW_Dist=mean(HW_Dist),
se_HW_Dist=sd(HW_Dist)/sqrt(n()))
bobwhite_means## # A tibble: 2 × 3
## HuntDay mean_HW_Dist se_HW_Dist
## <chr> <dbl> <dbl>
## 1 Quail 22.3 4.29
## 2 Rabbit 57.0 5.30mixed_bobwhite <- lmer(HW_Dist~(HuntDay*ID)+(1|ID), data = bobwhite)## Warning in as_lmerModLT(model, devfun): Model may not have converged with 1
## eigenvalue close to zero: 5.5e-09anova(mixed_bobwhite) ## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## HuntDay 19204.9 19204.9 1 188 11.0107 0.001088 **
## ID 3168.5 633.7 5 188 0.3633 0.873151
## HuntDay:ID 23341.2 4668.2 5 188 2.6764 0.023103 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1summary(mixed_bobwhite)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: HW_Dist ~ (HuntDay * ID) + (1 | ID)
## Data: bobwhite
##
## REML criterion at convergence: 1969
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.85694 -0.39986 -0.09686 0.24302 3.07350
##
## Random effects:
## Groups Name Variance Std.Dev.
## ID (Intercept) 3679 60.65
## Residual 1744 41.76
## Number of obs: 200, groups: ID, 6
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 16.6996 61.8382 188.0000 0.270 0.7874
## HuntDayRabbit 30.7117 14.0785 188.0000 2.181 0.0304 *
## ID2 -3.1075 87.2444 188.0000 -0.036 0.9716
## ID3 71.4500 87.7290 188.0000 0.814 0.4164
## ID4 -12.6545 87.8670 188.0000 -0.144 0.8856
## ID5 -0.6957 87.6185 188.0000 -0.008 0.9937
## ID6 -16.6996 87.8670 188.0000 -0.190 0.8495
## HuntDayRabbit:ID2 33.2485 19.1667 188.0000 1.735 0.0844 .
## HuntDayRabbit:ID3 -3.5830 21.1724 188.0000 -0.169 0.8658
## HuntDayRabbit:ID4 -31.1473 23.0762 188.0000 -1.350 0.1787
## HuntDayRabbit:ID5 -27.9975 22.5121 188.0000 -1.244 0.2152
## HuntDayRabbit:ID6 -22.5867 22.9181 188.0000 -0.986 0.3256
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) HntDyR ID2 ID3 ID4 ID5 ID6 HDR:ID2 HDR:ID3
## HuntDayRbbt -0.167
## ID2 -0.709 0.118
## ID3 -0.705 0.118 0.500
## ID4 -0.704 0.117 0.499 0.496
## ID5 -0.706 0.118 0.500 0.497 0.497
## ID6 -0.704 0.117 0.499 0.496 0.495 0.497
## HntDyRb:ID2 0.123 -0.735 -0.152 -0.086 -0.086 -0.087 -0.086
## HntDyRb:ID3 0.111 -0.665 -0.079 -0.183 -0.078 -0.078 -0.078 0.488
## HntDyRb:ID4 0.102 -0.610 -0.072 -0.072 -0.179 -0.072 -0.072 0.448 0.406
## HntDyRb:ID5 0.104 -0.625 -0.074 -0.074 -0.073 -0.162 -0.073 0.459 0.416
## HntDyRb:ID6 0.103 -0.614 -0.073 -0.072 -0.072 -0.072 -0.180 0.451 0.408
## HDR:ID4 HDR:ID5
## HuntDayRbbt
## ID2
## ID3
## ID4
## ID5
## ID6
## HntDyRb:ID2
## HntDyRb:ID3
## HntDyRb:ID4
## HntDyRb:ID5 0.382
## HntDyRb:ID6 0.375 0.384performance::check_model(mixed_bobwhite)
\(~\) \(~\)
Nested Hierarchical Model
Great Tits (Parus major)
Advertisement signaling is usually linked to intersexual selection and intrasexual competition and thus is a key component of a species’ ecology. Using a novel spatial tracking system, the authors tested whether or not the spatial behavior of male and female great tits (Parus major) changes in relation to the response of a territorial male neighbor to an intruder. They tracked the spatial behavior of male and female great tits (N = 20), 1 hr before and 1 hr after simulating territory intrusions.
tit <- read.csv("great_tits.csv")
tit$sex <- as.factor(tit$sex)
ggplot(tit, aes(sex, dist_m, colour = as.factor(id), shape=as.factor(measure))) +
geom_jitter(width =0.15, size=5, alpha=0.6)+
ylab ("Response Distance from Playback Location (meters)") +
xlab ("Sex") +
annotate("text", x = 2, y = 76, label = "20 birds") +
annotate("text", x = 2, y = 72, label = "2 measurements per bird") +
annotate("text", x = 2, y = 67, label = "40 total measurements", size=4, color="blue")+
labs(title="Sex-specific Responses to Territorial Intrusions", caption="1 = female
2 = male")+
theme_bw()
In this study, 20 individuals were measured 2 times, 1 hour before playback and 1 hour after. The individuals are separated by sex to look at the different distances between females and males. Distance on the Y axis is measured in meters, with distance being how many meters away a bird was detected before and after a playback recording was played of a territorial male’s song. Based on the measurements of distance before and after playback, it looks like there isn’t really a pattern of whether or not sex plays a role in an individual bird’s movement after a territorial playback.
lmmtit <- lmer(dist_m ~ sex + (1|sex/id), data = tit)
summary(lmmtit)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: dist_m ~ sex + (1 | sex/id)
## Data: tit
##
## REML criterion at convergence: 220.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.3793 -0.5409 -0.0890 0.4035 1.6695
##
## Random effects:
## Groups Name Variance Std.Dev.
## id:sex (Intercept) 258.264 16.071
## sex (Intercept) 4.187 2.046
## Residual 99.407 9.970
## Number of obs: 28, groups: id:sex, 14; sex, 2
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 28.838 6.533 14.604 4.414 0.000534 ***
## sex2 -2.629 9.909 14.236 -0.265 0.794568
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr)
## sex2 -0.659
## optimizer (nloptwrap) convergence code: 0 (OK)
## unable to evaluate scaled gradient
## Hessian is numerically singular: parameters are not uniquely determinedanova(lm(dist_m ~ sex/id, data = tit))## Analysis of Variance Table
##
## Response: dist_m
## Df Sum Sq Mean Sq F value Pr(>F)
## sex 1 47.4 47.40 0.1309 0.7207
## sex:id 2 90.6 45.31 0.1251 0.8830
## Residuals 24 8692.3 362.18